A generalized Douglas ADI method for solving three‐dimensional parabolic differential equations on multilayers

Develops a generalized Douglas ADI method for solving three‐dimensional parabolic differential equations based on the idea of the regularized difference scheme. The method is simple, unconditionally stable and well suited for either simulating fast transient phenomena or for computations on fine spatial meshes. Numerical procedures that employ the generalized Douglas ADI scheme were developed to solve three‐dimensional parabolic differential equations on multilayers. In these procedures, the generalized “divide and conquer” method for solving tridiagonal linear systems is applied in order to overcome the problem with the unknown value at the interface between layers. Numerical results show that the procedure is accurate and efficient.